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Math Help - region R - need your explaination.

  1. #1
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    Question region R - need your explaination.

    Given z=x^2+y^2

    I have the following information for region R.
    R = (x,y) such that x^2 +(y-1/2)^2 < or = 1/4

    why R = ( r,theta) such that 0< or = r < or = sin theta ? I don't understand how r = sin theta. Could you please explain to me? Thank you very much.
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    Given z=x^2+y^2

    And also z=y
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by kittycat View Post
    Given z=x^2+y^2

    I have the following information for region R.
    R = (x,y) such that x^2 +(y-1/2)^2 < or = 1/4

    why R = ( r,theta) such that 0< or = r < or = sin theta ? I don't understand how r = sin theta. Could you please explain to me? Thank you very much.
    0 \le x^2 + \left( y - \frac 12 \right)^2 = x^2 + y^2 - y + \frac 14 \le \frac 14

    \Rightarrow 0 \le x^2 + y^2 \le y

    switch to polar coordinates

    \Rightarrow 0 \le r^2 \le r \sin \theta

    divide through by r

    \Rightarrow 0 \le r \le \sin \theta
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